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Alisiya [41]
4 years ago
5

Kayla's father throws Kayla a graduation party that costs $775. He pays the DJ $250, $75 for the cake, and $5 per party guest fo

r food. How many people were at the party?

Mathematics
1 answer:
Charra [1.4K]4 years ago
7 0

Answer:

90 people

Step-by-step explanation:

Total: $775

DJ: $250

Cake: $75

Unknown party guests each getting $5

Let the unknown be x

We can form an equation; <em>DJ + Cake + x number of party guests = $775</em>

<em>250 + 75 + 5x = 775</em>

<em>325 + 5x = 775</em>

Subtract 325 from <u>both sides of the equals sign</u>.

<em>5x = 450</em>

Make <em>x</em> the subject and divide both sides by 5

<em>x = 90</em>

There were 90 party guests.

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Find a matrix representation of the transformation L(x, y) = (3x + 4y, x − 2y).
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Answer:

\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}3&1\\4&-2\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

Step-by-step explanation:

The general matrix representation for this transformation would be:

\left[\begin{array}{cc}x&y\end{array}\right] * A = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

As the matrix A should have the same amount of rows as columns in the firs matrix and the same amount of columns as the result matrix it should be a 2x2 matrix.

\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

Solving the matrix product you have that the members of the result matrix are:

3x+4y = a*x + c*y

x - 2y = b*x + d*y

So the matrix A should be:

\left[\begin{array}{cc}3&1\\4&-2\end{array}\right]

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Step-by-step explanation:

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